Discrete math

A coin is flipped ten times. How many outcomes DO NOT HAVE three heads?

halp!

Would the answer be something like 10^-x or 10c3?

I'm a little confused.

do not have exactly three heads, or do not have at least three heads?

In the former case: 2^-10 * (10c0 + 10c1 + 10c2 + 10c4 + 10c5 + 10c6 + 10c7 + 10c8 + 10c9 + 10c10)

Latter: 2^-10 * (10c0 + 10c1 + 10c2).

the former case is what I believe is suppose to be the case.

Thanks anon!

is 2^10 - 10C3 equivalent?

>>4
Oh wow, I gave probabilities instead of number of outcomes, sorry. Correct answer is what you have. (Alternately, 10c0 + 10c1 + 10c2 + 10c4 + 10c5 + 10c6 + 10c7 + 10c8 + 10c9 + 10c10 = Sum[i=0,10](10ci) - 10c3 = 2^10 - 10c3.)